The present invention relates to a digital filter device.
Low-pass filters, high-pass filters, band-pass filters and so on have conventionally been used as digital filters.
The first stage in designing the digital filter is to obtain its transfer function H(z). This transfer function H(z) may be obtained with respect to either the frequency or the time. Each of these methods may be further divided into FIR (finite impulse response type) according to which the handling of the impulse response of the digital filter is terminated at a finite limit, and IIR (infinite impulse response type) according to which this handling is continued indefinitely. The IIR type filter is further divided into several kinds according to design. Among them are filters which are designed to perform as analog filters, the transfer function H(S) of the analog filter is obtained, and this transfer function H(S) unergoes a transform such as the standard z-transform, the bilinear z-transform, or the alignment z-transform.
FIG. 1 shows an example of the frequency characteristic curve of an analog low-pass filter. This characteristic curve corresponds to the magnitude-squared response of a Butterworth filter. The method for performing the bilinear z-transform of H(S) of the analog filter of this type to obtain the transfer function H(z) may be described as follows. The poles of the Butterworth filter having the characteristic shown in FIG. 1 have conjugate roots such as P1 and P2 shown in FIG. 2. The analog transfer function H1(S) of this filter is given by ##EQU1## where S is the Laplace variable. Therefore, the transfer function of the low-pass filter with the cutoff frequency fc may be obtained as ##EQU2## by replacing S in equation (1) with S/.omega.c (.omega.c=2.pi.fc: angular frequency).
The transfer function H(z) of the digital filter may be obtained by performing the transform ##EQU3## for the variable S of the analog transfer function H(S). In equation (3), T is the sampling time and z is the variable of the bilinear z-transform. When equation (3) is substituted in equation (2), the transfer function H(z) may be given as ##EQU4## The frequency distortion in the S-z transform is considered here. When z=e.sup.j.omega.DT is substituted in equation (3), we have the following equation ##EQU5## where .omega.a is the angular frequency in the S-plane and .omega.D is the angular frequency in the z-plane. It is seen from equation (5) that, with higher frequencies, increasing distortion is caused by the S-z transform. When .omega.a=.omega.c in equation (5), .omega.c is given as ##EQU6## When tan (.omega.DT/2)=A in equation (6), equation (4) may be rewritten as ##EQU7## Making the following simplifications, ##EQU8## equation (7) may be rewritten as ##EQU9## A digital circuit having the transfer function satisfying equation (8) will comprise a desired digital Butterworth filter.
FIG. 3 shows the construction of a digital filter device having a transfer function according to equation (8). In FIG. 3, an input signal is supplied to an adder 1. An output of the adder 1 is supplied to an adder 2 as well as to a delay element 3 with a delay time T. An output of the delay element 3 is supplied to input terminals of multipliers 4 and 5. A coefficient b1 of a ROM 6 is supplied to a multiplication coefficient input terminal of the multiplier 4. An output of the multiplier 4 is supplied to a negative input terminal of the adder 1. An output of the multiplier 5 is supplied to a positive input terminal of the adder 2. The output of the delay element 3 is further supplied to a delay element 7 of the delay time T whose output is supplied to a multiplier 8 and the adder 2. A coefficient b2 is supplied to the multiplier 8 from the ROM 6. An output of the multiplier 8 is supplied to another negative input terminal of the adder 1. A digital signal representing the cutoff frequency fc of the filter is supplied to the ROM 6. The ROM 6 is so constructed as to selectively output the coefficients b1, b2, and K.sub.L of various values of equation (8) in response to the input of fc according to its various values. An output of the adder 2 is supplied to a multiplier 9 together with the output K.sub.L of the ROM 6, and the multiplier 9 outputs an output signal of the filter. A low-pass filter having the transfer function H(z) as given by equation (8) is thus constructed as shown in FIG. 3.
In a digital filter device of such a construction, the values of the coefficients b1, b2 and K.sub.L in the ROM 6 selected by the cutoff frequency fc increase as the cutoff frequency fc increases. The storage capacity of the ROM 6 must correspondingly be made larger.
Although the description has been made with reference to a digital low-pass filter, the same applies to a high-pass filter or a band-pass filter. The transfer function of a band-pass filter is more complex than that of a low-pass filter or a high-pass filter, and the required storage capacity of the ROM for storing the coefficients is correspondingly larger.
The ROM occupies a relatively large area on the semiconductor chip when integrating a digital filter. Therefore, the larger area occupied by the ROM results in less area for other elements and wirings, adversely affecting the multi-functional property of the digital filter.
It is, therefore, an object of the present invention to provide a digital filter device according to which the storage capacity of a memory for storing coefficients may be minimized and a higher packaging density may be realized without degrading the function of the digital filter.